Finite Group Databasebeta

← #14664231

Subgroups — #14664231

Order 2816.

500 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074175C211yesmaximal, characteristic
2#13068347C211yesmaximal, characteristic, complemented
3#13066947C211yesmaximal, characteristic, complemented
4#13066641C211yesmaximal, characteristic, complemented
5#13066639C211yesmaximal, characteristic, complemented
6#13066613C211yesmaximal, characteristic
7C11×#1343C211yesmaximal, characteristic
8C2×D4×Dic11C411yescharacteristic, complemented
9C2×#66930—21no—
10C2×#66930C2211yescharacteristic
11C11×#392C2211yescharacteristic
12#10622835C411yescharacteristic, complemented
13#10622833—21no—
14#10622833—21no—
15#10622562C2211yescharacteristic
16#10622559—21no—
17#10622558—21no—
18#10622332—21no—
19#10622272C411yescharacteristic, complemented
20#10622264C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11D411yescharacteristic
40D4×Dic11—41no—
41D4×Dic11—41no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—41no—
45C2×Dic11⋊C4C2×C411yescharacteristic
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11—41no—
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50#66930—24no—
51#66930—41no—
52#66930—41no—
53#66930—42no—
54C11×C22⋊C8—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66879—41no—
63Dic11⋊C8—41no—
64#11754—111nomaximal, Sylow
65C24×C11—21no—
66C24×C11C2×D411yescharacteristic
67C2×D4×C11—41no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—81no—
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—22no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—41no—
85C22×Dic11—42no—
86C22×Dic11—81no—
87C22×Dic11—81no—
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C22×Dic11C22⋊C411yescharacteristic
92C2×C8×C11—41no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—81no—
97C22⋊Dic11—22no—
98C22⋊Dic11—41no—
99C22⋊Dic11—42no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102C22⋊Dic11—42no—
103C22⋊Dic11—41no—
104C22⋊Dic11—81no—
105C4⋊Dic11—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—44no—
109Dic11⋊C4—81no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—44no—
115C2×C11⋊C8—41no—
116#2598—111no—
117#1740—111no—
118#1464—111no—
119#1352—111no—
120#1352—111no—
121#1343—111no—
122#1343D1111yescharacteristic
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—22no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11C2×C22⋊C411yescharacteristic
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136C23×C11#13711yescharacteristic
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140D4×C11—82no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—84no—
171C2×Dic11—81no—
172C2×Dic11—81no—
173C2×Dic11#9911yescharacteristic
174C2×Dic11#9911yescharacteristic
175C2×Dic11#10412yes—
176C8×C11—81no—
177C11⋊C8—81no—
178C2×C4×D4—111no—
179C2×#117—111no—
180C2×#117—221no—
181#432—221no—
182#400—111no—
183#399—111no—
184#394—111no—
185#392C2×D1111yescharacteristic
186#388—221no—
187#386—221no—
188#386—221no—
189#385—221no—
190#383—111no—
191#342—111no—
192#342—221no—
193#342C2×D1111yescharacteristic
194#324—221no—
195#323—111no—
196#323C2×D1111yescharacteristic
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—42no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11C2×#9911yescharacteristic
214C22×C11#41711yescharacteristic
215C22×C11C2×#10411yescharacteristic
216C4×C11—41no—
217C4×C11—41no—
218C4×C11—81no—
219C4×C11—82no—
220Dic11—21no—
221Dic11—21no—
222Dic11—22no—
223Dic11—41no—
224Dic11—41no—
225Dic11—81no—
226Dic11—82no—
227Dic11—81no—
228C22×D4—21no—
229C22×D4C4×D1111yescharacteristic
230C23×C4—111no—
231C23×C4—221no—
232C4×D4—441no—
233C4×D4—441no—
234#117—224no—
235#117—441no—
236#117—441no—
237#117—442no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—441no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4C22×D1111yescharacteristic
252C2×C42—111no—
253C2×C42—111no—
254C2×C42—441no—
255C4⋊C8—441no—
256C22⋊C8—21no—
257C22⋊C8—221no—
258#97—441no—
259#95—111no—
260#95—221no—
261#95—221no—
262#95—221no—
263#95—221no—
264#95C4×D1111yescharacteristic
265C2×C11—21no—
266C2×C11—21no—
267C2×C11—41no—
268C2×C11—41no—
269C2×C11—82no—
270C2×C11#150411yescharacteristic
271C2×C11#212011yescharacteristic
272C2×C11#212811yescharacteristic
273C24—21no—
274C24D4×D1111yescharacteristic
275C2×D4—41no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—81no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—222no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—442no—
295C22×C4—441no—
296C22×C4—881no—
297C22×C4—881no—
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C2×C8—41no—
301C2×C8—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—444no—
306C4⋊C4—881no—
307C22⋊C4—22no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—81no—
311C22⋊C4—222no—
312C22⋊C4—441no—
313C22⋊C4—441no—
314C22⋊C4—442no—
315C22⋊C4—441no—
316C22⋊C4—442no—
317C22⋊C4—441no—
318C22⋊C4—881no—
319C42—221no—
320C42—221no—
321C42—221no—
322C42—221no—
323C42—444no—
324C11#1175411yescharacteristic, complemented, Sylow
325C23—21no—
326C23—21no—
327C23—22no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23C22⋊C4×D1111yescharacteristic
337C23#6696411yescharacteristic
338C23#6696811yescharacteristic
339D4—42no—
340D4—42no—
341D4—82no—
342D4—82no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—111no—
354C2×C4—111no—
355C2×C4—112no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—442no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—884no—
376C2×C4—881no—
377C2×C4—881no—
378C8—81no—
379C8—881no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—42no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22D11×#9911yescharacteristic
397C22#1062238411yescharacteristic
398C22D11×#10411yescharacteristic
399C4—41no—
400C4—41no—
401C4—81no—
402C4—82no—
403C4—221no—
404C4—221no—
405C4—222no—
406C4—441no—
407C4—441no—
408C4—881no—
409C4—882no—
410C4—881no—
411C2—21no—
412C2—21no—
413C2—41no—
414C2—41no—
415C2—82no—
416C2#1306711711yescharacteristic
417C2#1307025411yescharacteristic
418C2#1307028611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1343C2
socleC22×C11C2×#99
prime radicalC11×#392C22
cosocleC2×C11×C22⋊C4C23
hypercenter#1343D11
hypocenterC11#11754
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13068347C2semidirect
3. #13066947C2semidirect
4. #13066641C2semidirect
5. #13066639C2semidirect
8. C2×D4×Dic11C4semidirect
12. #10622835C4semidirect
19. #10622272C4semidirect
20. #10622264C4semidirect
324. C11#11754semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130741752
#130683472
#130669472
#130666412
#130666392
#130666132
C11×#13432
#1175411